Answer
27,633
Work Step by Step
To form a committee of 6 members from a pool of 25 people, there are a total of 25C6 ways, which is equal to 177,100.
Now, we need to count the number of ways to form a committee with more women than men. This can be done by considering the following cases:
Case 1: The committee has 5 women and 1 man.
There are 15C5 ways to choose 5 women from the 15 available, and 10C1 ways to choose 1 man from the 10 available. So, there are 15C5 x 10C1 = 3,003 ways to form a committee with 5 women and 1 man.
Case 2: The committee has 4 women and 2 men.
There are 15C4 ways to choose 4 women from the 15 available, and 10C2 ways to choose 2 men from the 10 available. So, there are 15C4 x 10C2 = 13,230 ways to form a committee with 4 women and 2 men.
Case 3: The committee has 3 women and 3 men.
There are 15C3 ways to choose 3 women from the 15 available, and 10C3 ways to choose 3 men from the 10 available. So, there are 15C3 x 10C3 = 11,400 ways to form a committee with 3 women and 3 men.
Therefore, the total number of ways to form a committee with more women than men is 3,003 + 13,230 + 11,400 = 27,633.
So, there are 27,633 ways to form a committee with six members if it must have more women than men
